If one had to choose between the Sergeant Audie Murphy Club and a master's degree, which would you pick?

Masters unfortunately goes further than Audie Murphy on covvie side

You can do both. It may take longer than you would like to achieve both but it's possible and it's worth it.

Go for both no half measures

A Master's degree clearly takes you beyond the Military.

Master's Degree...anyone thinking there is a comparison is in need of professional help and they better stay in the military until they are kicked out.

Audie Murphy club.

No disrespect to members of the Sergeant Audie Murphy Club, but if I had to choose one or the other, I would choose a master's degree. It will benefit you the rest of your life, including your post-military life. Do you have to choose? Why not do both?

Master's Degree every time.

While both are great accomplishments, my Masters helps feed the family right now -- post Army career. If, however, you've got a ways to go prior to retirement and the opportunity presents itself to go for SAMC - go for it; and then focus upon completing your Masters prior to retiring.

I think folks have lost the focus of what SAMC started out as. SAMC was an organization that was meant to set apart those NCOs in the formation that truly were the cream of the crop. They were to be identified by their company leadership because of their outstanding performance and care for Soldiers, not self nominated to go to the board ( Audie was a humble man....). These selected NCOs were elevated to the post level so their spheres of influence would have a wider impact. They were to be the measuring stick the Post/Division CSM used for what an excellent NCO was. They would do community service to benefit the Soldier community and post.
As a SFC you should already be generating the sphere of influence SAMC would give you. As a SFC, there should not be to much studying to be done to be selected. As a SFC you have to be able to walk into that board and leave the board with the same exact feeling on what type of leader you are. You should not need SAMC to get promoted to MSG. The things you are enabling your soldiers to do and their band of excellence in performance should be your medallion for promotion.
Go get your Master's Degree. That will set you further apart from your peers.